math/big: fix Int.Exp

Fixes #7814.

LGTM=agl, adonovan
R=agl, adonovan
CC=golang-codereviews
https://golang.org/cl/90080043

src/pkg/math/big/int.go

@@ -576,21 +576,22 @@ func (x *Int) BitLen() int {
 }
 
 // Exp sets z = x**y mod |m| (i.e. the sign of m is ignored), and returns z.
-// If y <= 0, the result is 1; if m == nil or m == 0, z = x**y.
+// If y <= 0, the result is 1 mod |m|; if m == nil or m == 0, z = x**y.
 // See Knuth, volume 2, section 4.6.3.
 func (z *Int) Exp(x, y, m *Int) *Int {
-	if y.neg || len(y.abs) == 0 {
-		return z.SetInt64(1)
+	var yWords nat
+	if !y.neg {
+		yWords = y.abs
 	}
-	// y > 0
+	// y >= 0
 
 	var mWords nat
 	if m != nil {
 		mWords = m.abs // m.abs may be nil for m == 0
 	}
 
-	z.abs = z.abs.expNN(x.abs, y.abs, mWords)
-	z.neg = len(z.abs) > 0 && x.neg && y.abs[0]&1 == 1 // 0 has no sign
+	z.abs = z.abs.expNN(x.abs, yWords, mWords)
+	z.neg = len(z.abs) > 0 && x.neg && len(yWords) > 0 && yWords[0]&1 == 1 // 0 has no sign
 	return z
 }
 

src/pkg/math/big/int_test.go

@@ -768,6 +768,19 @@ var expTests = []struct {
 	x, y, m string
 	out     string
 }{
+	// y <= 0
+	{"0", "0", "", "1"},
+	{"1", "0", "", "1"},
+	{"-10", "0", "", "1"},
+	{"1234", "-1", "", "1"},
+
+	// m == 1
+	{"0", "0", "1", "0"},
+	{"1", "0", "1", "0"},
+	{"-10", "0", "1", "0"},
+	{"1234", "-1", "1", "0"},
+
+	// misc
 	{"5", "-7", "", "1"},
 	{"-5", "-7", "", "1"},
 	{"5", "0", "", "1"},

src/pkg/math/big/nat.go

@@ -1233,10 +1233,15 @@ func (z nat) expNN(x, y, m nat) nat {
 		z = nil
 	}
 
+	// x**y mod 1 == 0
+	if len(m) == 1 && m[0] == 1 {
+		return z.setWord(0)
+	}
+	// m == 0 || m > 1
+
+	// x**0 == 1
 	if len(y) == 0 {
-		z = z.make(1)
-		z[0] = 1
-		return z
+		return z.setWord(1)
 	}
 	// y > 0
 

src/pkg/math/big/nat_test.go

@@ -714,6 +714,12 @@ var expNNTests = []struct {
 	x, y, m string
 	out     string
 }{
+	{"0", "0", "0", "1"},
+	{"0", "0", "1", "0"},
+	{"1", "1", "1", "0"},
+	{"2", "1", "1", "0"},
+	{"2", "2", "1", "0"},
+	{"10", "100000000000", "1", "0"},
 	{"0x8000000000000000", "2", "", "0x40000000000000000000000000000000"},
 	{"0x8000000000000000", "2", "6719", "4944"},
 	{"0x8000000000000000", "3", "6719", "5447"},
@@ -741,7 +747,7 @@ func TestExpNN(t *testing.T) {
 
 		z := nat(nil).expNN(x, y, m)
 		if z.cmp(out) != 0 {
-			t.Errorf("#%d got %v want %v", i, z, out)
+			t.Errorf("#%d got %s want %s", i, z.decimalString(), out.decimalString())
 		}
 	}
 }